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I'm currently working on a Python Program which aim to return the secret key rate of a specific Quantum Key Distribution protocol (Brassard, Benett and Mermin 1992 i.e. BBM92). A colleague will provide me with the result of this protocol. However, I am still looking for the right formalism to express this secure key rate.
So, are there existing formalism(s) to to express the secure key rate?

And optionally: Do they have public software support?

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    $\begingroup$ Please note that request for software / library recommendations are off-topic for this site and only on-topic on Software Recommendations. However your other question is still interesting so I have shifted the focus via an edit a bit. $\endgroup$
    – SEJPM
    Commented Jun 11, 2020 at 11:12
  • $\begingroup$ Perhaps the paper linked at end of section B.1 of this answer will help. $\endgroup$
    – fgrieu
    Commented Jun 11, 2020 at 19:55

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The BBM92 paper discusses that it is, in fact, exactly equivalent to the BB84 protocol. It is not discussed in the paper, but that would naturally imply that the key-rate equation is the same for BBM92 and BB84.

The key-rate of BB84, in the asymptotic case where you assume that observed noise is exactly correct (i.e. no statistical noise due to an asymptotically large sample) is $r=1-2h(Q)$ where $Q$ is the quantum bit error rate and $h(x) = -x\log_2x - (1-x)\log_2(1-x)$.

In practice you would likely want to look into it's key rate in the finite key length regime, where (roughly speaking) you minimize the key-rate over a confidence interval surrounding the observed noise rate $Q$.

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